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3 years ago

When you are given two angle measures and the length of the included side, do you get a unique triangle

Mathematics

1 answer:

Alenkasestr [34]3 years ago

8 0

Yes ...you get a unique triangle.

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Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rho(x, y) = 2x + 2y + 2x2 + 2y

professor190 [17]

Answer:

Required total charge is $256\pi$ coulombs per square meter.

Step-by-step explanation:

Given electric charge is dristributed over the disk,

$x^2=y^2\leq 16$ so that the charge density at (x,y) is,

$\rho (x,y)=2x+2y+2x^2+2y^2$

To find total charge on the disk let Q be the total charge and $x=r\cos\theta,y=r\sin\theta$ so that,

$Q={\int\int}_Q\rho(x,y) dA$ where A is the surface of disk.

$=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA$

$=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta$

$=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta$

$=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta$

$=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta$

$=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi$

$=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi$

$=256\pi$

Hence total charge is $256\pi$ coulombs per square meter.

3 0

3 years ago

What value of g makes the equation 2g+6-14g=-6(g-5) true?

Sergeu [11.5K]

Answer:

g=-4

Step-by-step explanation:

2g+6-14g=-6(g-5)

-12g+6=-6g+30

-6g+6=30

-6g=24

g=-4

8 0

3 years ago

Plz tell me someone know how to do this!!<br> I'll mark brainliest

anygoal [31]

Answer:

It would be the second option

Step-by-step explanation:

z:28 is the ratio of the shorter triangle's side to the larger triangle's side, so is 27:45.

5 0

2 years ago

The difference between the acute angles of a right angled triangle is 72degree find them .

MaRussiya [10]

The 2 angles add up to 90 degrees so

x + y = 90, also:-

x - y = 72 (given)

adding the 2 equations:-

2x = 162

x = 81

and therefore

y + 81 = 90

y = 9

Answer the 2 angles are 81 and 9 degrees

5 0

2 years ago

Michelle and her father want to make a triangular sail for their boat. The height of the sail will be 24 ft., and the base will

Lemur [1.5K]

Answer:

The area of the triangular sail is 216 ft²

Step-by-step explanation:

Since the sail is triangular, we solve the area using the area of a triangle

Area of triangle = 1/2 of base × height

base is 18 and height is 24

Area = 1/2 × 18 × 24

= 9×24

= 216 ft²

5 0

3 years ago